Least Common Multiple (LCM) of 123 and 167
The least common multiple (LCM) of 123 and 167 is 20541.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 123 and 167?
First, calculate the GCD of 123 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 167 = 0 remainder 123 |
| 2 | 167 ÷ 123 = 1 remainder 44 |
| 3 | 123 ÷ 44 = 2 remainder 35 |
| 4 | 44 ÷ 35 = 1 remainder 9 |
| 5 | 35 ÷ 9 = 3 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 69 | 3657 |
| 193 and 119 | 22967 |
| 69 and 27 | 621 |
| 103 and 26 | 2678 |
| 142 and 72 | 5112 |